CTSBS Age-Mixing

Research questions:

Describe the age-mixing pattern in the CTSBS population. Does the age-mixing pattern of HIV positive participants differ from the general population?
At the individual-level are large ranges in partner ages (bridgewidths) associated with HIV status of a participant?
Large bridgewidths may make it possible for participants to acquire HIV from one age group and transmit to the next, but are they also associated with risky sexual behaviours among participants?

Before conducting imputations, I excluded participants who said their sexual preferences were for “both” genders or the same gender (n = 76). I further excluded people who did not identify as black or coloured (n = 7) and people who did not report partners in the previous year (n = 170). Participants who had missing observations on those characteristics were left in the dataset. This left 1074 relationships reported by 647 participants. Of the 647 participants, 185 reported more than one relationship in the previous year. I imputed 50 datasets using the random forest method for continuous and nominal categorical variables and the “polr” method for our ordinal variables.

AGE-MIXING PATTERN

Here I used linear mixed effects models that were stratified by sex and contained a random intercept for the participant. For the plots, I randomly selected an imputed dataset to visualize the pattern in that population. I did not explicitly model heteroskedastic variance, like we did with the LNS data, because plots of the residuals did not seem to indicate increasing variance with age.

Figure 1. Age mixing pattern for randomly selected imputed dataset. The top row represents the male and female age mixing patterns HIV negative study population, while the bottom row is for only those with HIV

Figure 2. Extractions of model slopes, intercepts, intercept variance and residual variance for each imputed dataset. The top row represents the male and female age mixing patterns in the whole study population, while the bottom row is for only those with HIV

For some of the models on the some datasets (e.g. impution 9 in the HIV positive female sub-population), I recieved this error message when trying to obtain the CIs for the between-subject (intercept) SD: “cannot get confidence intervals on var-cov components: Non-positive definite approximate variance-covariance”. According to Jose Pinheiro, this “indicates that, although the optimization algorithm converged (according to the criteria defined in the ms() function), the Hessian matrix calculated at the converged values was not negative-definite and therefore an approximate covariance matrix for the MLE’s could not be obtained. This is generally caused by a flat log-likelihood surface, for which the algorithm decided that no further improvements were possible and declared convergence. This is an indication that the model may be overparameterized and that you should cut down in the number of parameters.”

In the power variance function coefficient plot, there were 20 imputations removed because “Non-positive definite approximate variance-covariance”.

DO BRIDGEWIDTHS AND SD’S GROW WITH AGE?

	Male				Female
Table 1. Mean bridgewidth by age category and gender in randomly selected imputed dataset
Age category	n	Mean	SD	SEM	n	Mean	SD	SEM
15-24	37	3.38	4.54	0.75	82	3.26	10.33	1.14
25-34	49	3.84	7.62	1.09	157	1.13	4.16	0.33
35-44	42	1.67	3.97	0.61	120	1.40	5.37	0.49
45-54	48	3.65	9.63	1.39	49	0.82	3.24	0.46
55-70	33	3.64	9.17	1.60	29	4.34	12.15	2.26
SD, Standard Deviation SEM, Standard Error of the Mean

DOES HIV STATUS PREDICT BRIDGEWIDTH?

Here I used generalised additive models with negative binomial regression to regress bridgewidths on HIV status of the participant before enterring our study. In these models, the participant is the unit of observation and only participants reporting more than one partner in the previous year were included. Separate models were created for men and women, as well as imputed datasets. The models adjust for age(smooth term) and race.

Figure 3. Distribution of bridge widths for each imputed dataset, by sex and HIV status.

Figure 4. Model coefficients for relationship between HIV and bridgewidth.

Figure 5. Expected bridge widths for different values of age (smooth term), by gender.

ARE LARGE BRIDGEWIDTHS ASSOCIATED WITH PARTICIPANTS HAVING A CONCURRENT RELATIONSHIP IN THE PREVIOUS YEAR?

Here, I regressed a binary partnership-level concurrency indicator on bridgewidths using a generalized additive logistic regression model. Again, the participant was the unit of observation and only participants reporting more than one relationship in the previous year were included. Models were applied to different imputed datasets and stratified by gender. All models adjust for age(smooth term) and race. Bridgewidth was treated as a continuous linear term because exploration using GAMS indicated it should be.

Figure 6. Distribution of the percentage of participants who had a concurrent relationship in the previous year, stratified by gender and across all imputations.

Figure 7. Effect of bridgewidth (Odds Ratios, OR) on whether a participant had a concurrent relationship in the previous year, stratified by gender.

Figure 8. Predicted probabilities of having had a concurrent relationship in the year before the survey for different values of age, by gender.

The following plots, visualize models where we are interested in the effect of whether the HIV status of a participant was associated with them having a subsequent concurrent relationship (but in the year before the survey). In these models HIV was our exposure of interest, and bridgewidth a hypothesized mediator. Again these were adjusted for age(smooth term) and race.

Figure 9. Effect of HIV (Odds Ratios, OR) on whether a participant had a concurrent relationship in the year before the survey, stratified by gender. Many confidence intervals and ORs are not showing because there were huge, inflated CI’s that were outside the limits of the y-axis.

Figure 10. Effect of bridgewidth (Odds Ratio, OR) on whether a participant had a concurrent relationship in the year before the survey, stratified by gender.

Figure 11. Predicted probabilities of having had a concurrent relationship in the previous year for different values of age (smooth term), by gender.

ARE LARGE BRIDGWIDTHS ASSOCIATED WITH USING ALWAYS USING CONDOMS IN A RELATIONSHIP?

I regressed a binary relationship-level condom use indicator on bridgewidths using a generalized additive mixed models with a logistic outcome and random intercept for participant. The relationship was the unit of observation and only relationships from participants reporting more than one relationship in the previous year were included. Models were applied to different imputed datasets and stratified by gender. All models adjust for age(smooth term) and race. Bridgewidth was treated as a continuous linear term because exploration using GAMS indicated it should be.

Figure 12. Distribution of the proportions of relationships using condoms, stratified by sex and across all imputations

Figure 13. Effect of bridgewidth (Odds Ratios, OR) on “Always” using a condom in relationship, stratified by gender.

Figure 14. Predicted probabilities of “Always” using a condom in a relationship for different ages of participant, stratified by gender.

The following plots, visualize models where we are interested in the effect of whether the HIV status of a participant was associated with always using a condom in relationships. In these models HIV was our exposure of interest, and bridgewidth a hypothesized mediator. Again these were adjusted for age(smooth term) and race.

Figure 15. Effect of HIV (Odds Ratios, OR) on “Always” using a condom in relationship, stratified by gender.

Figure 16. Effect of bridgewidth (Odds Ratios, OR) on “Always” using a condom in relationship, stratified by gender.

Figure 17. Predicted probabilities of “Always” using a condom in a relationship for different ages of participant, stratified by gender.

ARE LARGE BRIDGEWIDTHS ASSOCIATED WITH HIGHER SEX FREQUENCY IN RELATIONSHIPS?

I regressed sex frequency on bridgewidth. Sex frequency is a relationship-level variable that represents the average number of times a participant had sex per week with that partner. I used generalized additive mixed models with a poisson outcome and random intercept for participant. The relationship was the unit of observation and only relationships from participants reporting more than one relationship in the previous year were included. Models were applied to different imputed datasets and stratified by gender. All models adjust for age(smooth term) and race. Bridgewidth was treated as a continuous linear term because exploration using GAMS indicated it should be.

Figure 18. Distribution of average number of times sex occurred per week in relationships, stratified by gender and imputation dataset

Figure 19. Effect of bridgewidth (Incidence Rate Ratios, IRRs) on average number of times sex occurred per week in the relationship, stratified by gender.

Figure 20. Predicted average number of times sex occurred per week in a relationship for different ages of participant, stratified by gender.

The following plots, visualize models where we are interested in the effect of whether the HIV status of a participant was associated with sex frequency in relationships. In these models HIV was our exposure of interest, and bridgewidth a hypothesized mediator. Again these were adjusted for age(smooth term) and race.

Figure 21. Effect of HIV (Incidence Rate Ratios, IRR) on average number of times sex occurred per week in the relationship, stratified by gender.

Figure 22. Effect of bridgewidth (Incidence Rate Ratios, IRR) on average number of times sex occurred per week in the relationship, stratified by gender.